Bio111 Chapter 2 Flashcards

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The flow of a small stream is monitored for $90$ days between May $1$ and August $1$ . The total water that flows past a gauging station is given by

V(t)=\left\{\begin{array}{cl} \frac{4}{5} t^2 & \text { if } 0 \leq t<45 \\ -\frac{4}{5}\left(t^2-180 t+4050\right) & \text { if } 45 \leq t<90 \end{array}\right.

where $V$ is measured in cubic feet and $t$ is measured in days, with $t=0$ corresponding to May $1$ . a. Graph the volume function. b. Find the flow rate function $V^{\prime}(t)$ and graph it. What are the units of the flow rate? c. Describe the flow of the stream over the $3$ -month period. Specifically, when is the flow rate a maximum?